A few families took a trip to an amusement park together. Tickets cost $$8.00$ each for adults and $$4.50$ each for kids, and the group paid $$63.50$ in total. There were $3$ fewer adults than kids in the group. Find the number of adults and kids on the trip.
Solution: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${8x+4.5y = 63.5}$ ${x = y-3}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-3}$ for $x$ in the first equation. ${8}{(y-3)}{+ 4.5y = 63.5}$ Simplify and solve for $y$ $ 8y-24 + 4.5y = 63.5 $ $ 12.5y-24 = 63.5 $ $ 12.5y = 87.5 $ $ y = \dfrac{87.5}{12.5} $ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into ${x = y-3}$ to find $x$ ${x = }{(7)}{ - 3}$ ${x = 4}$ You can also plug ${y = 7}$ into ${8x+4.5y = 63.5}$ and get the same answer for $x$ ${8x + 4.5}{(7)}{= 63.5}$ ${x = 4}$ There were $4$ adults and $7$ kids.